Elements of the Theory of Markov Processes and Their ApplicationsGraduate-level text and reference in probability, with numerous scientific applications. Nonmeasure-theoretic introduction to theory of Markov processes and to mathematical models based on the theory. Appendixes. Bibliographies. 1960 edition. |
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Page 12
... matrix of transition probabilities : Poo Po1 P02 ... P10 P11 P12 P = P20 P21 P22 ∞ j = 0 = Clearly P is a square matrix ( of infinite order since the chain has a denumerable number of states ) with nonnegative elements , since pis > 0 ...
... matrix of transition probabilities : Poo Po1 P02 ... P10 P11 P12 P = P20 P21 P22 ∞ j = 0 = Clearly P is a square matrix ( of infinite order since the chain has a denumerable number of states ) with nonnegative elements , since pis > 0 ...
Page 14
... matrix associated with a decomposable chain can be written in the form of a partitioned matrix ; for example , 2 P = P1 0 ] P2 In the above , P1 and P2 represent Markov matrices which describe . the transitions within the two closed ...
... matrix associated with a decomposable chain can be written in the form of a partitioned matrix ; for example , 2 P = P1 0 ] P2 In the above , P1 and P2 represent Markov matrices which describe . the transitions within the two closed ...
Page 35
... matrix II when the matrix of transition probabilities P is given has been considered by many investigators using different methods ( cf. [ 17 ] ) . For the application of semigroup theory to this problem we refer to the paper of Kendall ...
... matrix II when the matrix of transition probabilities P is given has been considered by many investigators using different methods ( cf. [ 17 ] ) . For the application of semigroup theory to this problem we refer to the paper of Kendall ...
Contents
Introduction | 1 |
Processes Discrete in Space and Time | 9 |
Processes Discrete in Space and Continuous in Time | 57 |
Copyright | |
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Other editions - View all
Elements of the Theory of Markov Processes and Their Applications A. T. Bharucha-Reid Limited preview - 2012 |
Elements of the Theory of Markov Processes and Their Applications Albert T. Bharucha-Reid Limited preview - 1997 |
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absorber applications assume assumptions asymptotic birth process birth-and-death process boundary branching processes cascade process cascade theory coefficient collision consider counter defined denote the number denote the probability deterministic differential equation diffusion equations diffusion processes discrete branching process distribution function E₁ electron-photon cascades energy epidemic exists expression Feller finite functional equation given Hence initial condition integral equation interval 0,t ionization Kolmogorov equations Laplace transform Let the random machine Markov chain Markov processes Math mathematical matrix Mellin transform method Monte Carlo methods neutron nonnegative nucleon number of individuals o(At obtain P₁ photon Poisson process population probability distribution problem Proc product density queueing system r₁ radiation Ramakrishnan random variable random variable X(t random walk recurrent satisfies sequence Statist stochastic model Stochastic Processes t₁ t₂ Takács tion transition probabilities X₁ zero дх